1. Field of the Invention
The present invention relates to wideband RF communications systems, and more particularly to ultra-wideband (UWB) communications systems.
2. State of the Art
Ultra-Wideband Signals have been legal in the United States since February 2002 under conditions stipulated by the FCC Report and Order 02-48. Briefly, UWB signals must never be transmitted with a power spectral density of more than −41.2 dBm/MHz in a band from 3.1 GHz to 10.7 GHz. Elsewhere, the power must be reduced even further to protect existing services. Since the power limit is specified as a power spectral density, the transmit power is proportional to the bandwidth, and hence the desire is to occupy as much bandwidth as possible within economic and feasibility constraints and thereby maximize the possible link range. However, due to the increasing RF path loss with carrier frequency, as well as increasing noise figure of semiconductor devices, initial interest is concentrated on exploiting the spectrum from 3.1-4.9 GHz.
Two competing standards proposals for UWB have emerged, one identified with Motorola and the other identified with a coalition of companies referred to as the Multiband OFDM Alliance (MBOA). The MBOA-OFDM (hereinafter “MB-OFDM”) system borrows heavily from the existing wireless LAN concepts for 802.11a and 802.11g. The OFDM signal consists of 128 sub-carriers. These carriers occupy a 528 MHz, so the sub-carrier spacing is 4.125 MHz. Since the carrier spacing is 4.125 MHz, it follows that the OFDM symbol length must be 1/4.125e6=242.42 ns. To allow for inter-symbol interference a zero-energy prefix of ¼ of the symbol length (60.6 ns) is applied in place of the more traditional cyclic prefix. Finally a guard period of 5 samples (9.47 ns) is added. The total OFDM symbol length is 312.5 ns.
Of the 128 sub-carriers, 5 are set to nulls at the band edges, so that the actual occupied bandwidth is only 507.375 MHz (marginally wider than the mandated 500 MHz). Moreover, only 100 of the 128 sub-carriers are information-bearing; the others are either pilots, user-defined, or nulls. The 100 information-bearing tones carry QPSK modulation, thus providing 2 bits each, or 200 bits per OFDM symbol. The total gross information rate is thus (200/312.5e-9), or 640 Mbps. After channel coding redundancy is taken into account, the maximum protected data rate is 480 Mbps (¾ rate code).
As noted above the plain use of OFDM results in an occupied spectrum of just over 500 MHz, which is less than a third of the UWB spectrum available below 5 GHz. Since the transmitted power is proportional to the occupied bandwidth, failure to address this would have a serious impact on the available range. The MB-OFDM specification uses a 3-band hopping scheme to realize a 3-fold increase in bandwidth. The method adopted is that successive OFDM symbols are transmitted in different bands according to a predefined hopping sequence of length 6. These hopping sequences are designed to minimize collisions between uncoordinated piconets and are called Time-Frequency Interleaving (TFI) Codes. Example sequences include {1, 2, 3, 1, 2, 3}, {3, 2, 1, 3, 2, 1}, {1, 1, 2, 2, 3, 3} etc., where each index represents a specific 528 MHz frequency band.
The following table shows how PHY-SAP data rates from 53.3 to 480 Mbps are derived from the basic 640 Mbps uncoded bit rate.
DataCodingConjugateTimeOverallCoded bits perRaterateSymmetricSpreading FactorSpreadingOFDM symbol(Mb/s)Modulation(R)Input to IFFT(TSF)Gain(NCBPS)53.3QPSK⅓Yes2410055QPSK 11/32Yes2410080QPSK½Yes24100106.7QPSK⅓No22200110QPSK 11/32No22200160QPSK½No22200200QPSK⅝No22200320QPSK½No1 (No spreading)1200400QPSK⅝No1 (No spreading)1200480QPSK¼No1 (No spreading)1200
The three mechanisms for introducing redundancy are as follows:                1. Convolutional Coding with rates ⅓, 11/32, ½, ⅝ and ¾.        2. Conjugate Symmetric Input to the IFFT, which introduces a factor of ½.        3. Time spreading, where complete OFDM symbols may be repeated on different frequencies.        
All three of these techniques are briefly described in the following paragraphs.
Convolutional Coding
A 64-state convolutional encoder is used with 3 polynomials to create a ⅓-rate mother code. Puncturing of the output is used to adapt the code rate by reducing the redundancy. Different puncturing patterns are employed to obtained the specified rates according to the MB-OFDM specification. At the receiver, depuncturing is performed by inserting zeros in place of the punctured out bits, before processing by the Viterbi decoder.
Conjugate Symmetric Input to the IFFT
The sum of two complex exponential equal and opposite angular frequencies and complex conjugate coefficients can be shown as follows.
            1      ⁢              /            ⁢              2        ⁡                  [                                                    (                                  a                  +                  bj                                )                            ⁢                              exp                ⁡                                  (                                      jω                    ⁢                                                                                  ⁢                    t                                    )                                                      +                                          (                                  a                  -                                      b                    ⁢                                                                                  ⁢                    j                                                  )                            ⁢                              exp                ⁡                                  (                                                            -                      jω                                        ⁢                                                                                  ⁢                    t                                    )                                                              ]                      =                  1        ⁢                  /                ⁢                  2          ⁡                      [                                                            (                                      a                    +                    bj                                    )                                ⁢                                  (                                                            cos                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                              +                                          j                      ⁢                                                                                          ⁢                                              sin                        ⁡                                                  (                                                      ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                                                      )                                            +                                                (                                      a                    -                    bj                                    )                                ⁢                                  (                                                            cos                      ⁡                                              (                                                  ω                          ⁢                                                                                                          ⁢                          t                                                )                                                              -                                          j                      ⁢                                                                                          ⁢                                              sin                        ⁡                                                  (                                                      ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                                                      )                                                      ]                              =                        1          ⁢                      /                    ⁢                      2            ⁡                          [                                                a                  ⁢                                                                          ⁢                                      cos                    ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                      -                                  b                  ⁢                                                                          ⁢                                      sin                    ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                      +                                  j                  ⁡                                      (                                                                  b                        ⁢                                                                                                  ⁢                                                  cos                          ⁡                                                      (                                                          ω                              ⁢                                                                                                                          ⁢                              t                                                        )                                                                                              +                                              a                        ⁢                                                                                                  ⁢                                                  sin                          ⁡                                                      (                                                          ω                              ⁢                                                                                                                          ⁢                              t                                                        )                                                                                                                )                                                  +                                  a                  ⁢                                                                          ⁢                                      cos                    ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                      -                                  b                  ⁢                                                                          ⁢                                      sin                    ⁡                                          (                                              ω                        ⁢                                                                                                  ⁢                        t                                            )                                                                      -                                  j                  ⁡                                      (                                                                  b                        ⁢                                                                                                  ⁢                                                  cos                          ⁡                                                      (                                                          ω                              ⁢                                                                                                                          ⁢                              t                                                        )                                                                                              +                                              a                        ⁢                                                                                                  ⁢                                                  sin                          ⁡                                                      (                                                          ω                              ⁢                                                                                                                          ⁢                              t                                                        )                                                                                                                )                                                              ]                                      =                                            a              ⁢                                                          ⁢                              cos                ⁡                                  (                                      ω                    ⁢                                                                                  ⁢                    t                                    )                                                      -                          b              ⁢                                                          ⁢                              sin                ⁡                                  (                                      ω                    ⁢                                                                                  ⁢                    t                                    )                                                              =                                                                      a                  2                                +                                  b                  2                                                      ⁢                          cos              ⁡                              (                                                      ω                    ⁢                                                                                  ⁢                    t                                    +                  ϕ                                )                                                          ;      ϕ    =          arctan      ⁡              (                  b          ,          a                )            
The corresponding time sequence (the result of the IFFT) is thereby forced to be real, since it represents an integer number of cycles of a cosine wave of amplitude and phase defined by |a+bj| and angle(a+jb) respectively, as demonstrated by mathematical identities above.
The use of this principal in the MB-OFDM transmitter is as follows. There are allocated 100 complex QPSK symbols in the 128 pt IFFT. Initially, only 50 of these are filled with QPSK symbols corresponding to positive frequencies, the remaining 50 are copied to the negative frequency bins but with a complex conjugate operation. The FFT bins corresponding to d.c. and ±fs/2 are set to zero along with the four other null tones. Since the result of the IFFT is guaranteed to be entirely real, hardware simplifications can be realized in the transmitter (only the real arm of the quadrature upconversion need be realized, and certain arithmetic operations in the IFFT can be eliminated).
Time Spreading
For data rates of 53.3, 55, 80, 106.7, 110, 160 and 200 Mbps a time-domain spreading operation is performed with a spreading factor of two. The time-domain spreading operation consists of transmitting the same information over two OFDM symbols. These two OFDM symbols are transmitted over different sub-bands to obtain frequency diversity. For example, if the device uses a time-frequency code [1 2 3 1 2 3], the information in the first OFDM symbol is repeated on sub-bands 1 and 2, the information in the second OFDM symbol is repeated on sub-bands 3 and 1, and the information in the third OFDM symbol is repeated on sub-bands 2 and 3.
A block diagram of a known MB-OFDM UWB transmitter is shown in FIG. 1. Input data is first scrambled (block 101), then encoded (blocks 103, 105), then formed into data symbols and finally OFDM symbols (blocks 107, 109). The frequency-domain OFDM symbols are then transformed into a baseband time-domain signal (blocks 111, 113) and upconverted to an RF time-domain signal (blocks 115, 117) applied to an antenna 119. Note in block 111 (IFFT) the insertion of pilot tones and the addition of a cyclical prefix and a guard interval as explained previously. Further note in block 115 the application of a time-frequency code as explained previously.
A block diagram of a known MB-OFDM UWB receiver is shown in FIG. 2. The receiver is a quadrature receiver having an RF front end 230 including a I branch 210 and a Q branch 220. In block 240, an FFT is performed to transform the received time-domain signal back into a frequency-domain OFDM symbol; concurrently, synchronization is performed, and the cyclical prefix is removed. Block 251 is responsible for frequency domain equalization, which may be achieved, for example, by dividing each complex frequency-domain signal sample by its corresponding frequency-domain channel estimate. For best results the carrier phase estimate initially obtained from the pre-amble should be periodically updated by tracking algorithms (block 253) as the burst progresses. Blocks 207, 203 and 201 perform the inverse operations of blocks 107, 103 and 101.
In the foregoing MB-OFDM approach, although the average PDS of the signal over the course of a TFI code satisfies FCC requirements, as the time interval over which the average is calculated is shortened, an argument may be made that strict compliance with the requirements is not achieved. A need therefore exists for alternative approaches that achieve strict rules compliance while preserving the advantages of the MB-OFDM approach.